Moment closures velocity field

We shall see that transported PDF closures forthe velocity field are usually linear in V. Thus (/ D) will depend only on the first two moments of U. In general, non-linear velocity models could be formulated, in which case arbitrary moments of U would appear in the Reynolds-stress transport equation. 

The turbulence models discussed in this chapter attempt to model the flow using low-order moments of the velocity and scalar fields. An alternative approach is to model the one-point joint velocity, composition PDF directly. For reacting flows, this offers the significant advantage of avoiding a closure for the chemical source term. However, the numerical methods needed to solve for the PDF are very different than those used in standard CFD codes. We will thus hold off the discussion of transported PDF methods until Chapters 6 and 7 after discussing closures for the chemical source term in Chapter 5 that can be used with RANS and LES models. 

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